1 The following decision tree describes a decision problem involving survey information 300 di 20 X2 0.3 200 d2 100 X2 0.3 don't use survey 0.4 300 di 20 X2 a use survey survey cost: –5 0.4 200 d2 100 X2 a 82 1- q 300 di 20 X2 0.2 200 d2 100 X2 0.2 (a) Describe the specific probabilities that each variable a, b, p, q corresponds to, then deter- mine the value of each. (b) Solve the decision tree (using the EMV criterion, i.e. maximise the expected utility). (c) Determine the values of EMV (without the survey), EMV(survey), EVSI and ENGSI.

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1 The following decision tree describes a decision problem involving survey information
300
di
20
x2 0.3
xi p
200
d2
100
X2 0.3
don't use survey
0.4
300
di
20
X2 a
use survey
survey cost: -5
0.4
200
d2
S1
100
X2 a
82 1- q
300
di
20
X2 0.2
200
d2
100
X2 0.2
(a) Describe the specific probabilities that each variable a, b, p, q corresponds to, then deter-
mine the value of each.
(b) Solve the decision tree (using the EMV criterion, i.e. maximise the expected utility).
(c) Determine the values of EMV (without the survey), EMV(survey), EVSI and ENGSI.
Transcribed Image Text:1 The following decision tree describes a decision problem involving survey information 300 di 20 x2 0.3 xi p 200 d2 100 X2 0.3 don't use survey 0.4 300 di 20 X2 a use survey survey cost: -5 0.4 200 d2 S1 100 X2 a 82 1- q 300 di 20 X2 0.2 200 d2 100 X2 0.2 (a) Describe the specific probabilities that each variable a, b, p, q corresponds to, then deter- mine the value of each. (b) Solve the decision tree (using the EMV criterion, i.e. maximise the expected utility). (c) Determine the values of EMV (without the survey), EMV(survey), EVSI and ENGSI.
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